| The finite sample properties of estimators in some moment condition models often differ substantially from the approximations provided by asymptotic theory. The bootstrap can provide a way to circumvent the inadequacies of asymptotic approximations, but in over identified models, where the dimension of the parameter is smaller than the number of moment conditions, the usual uniform bootstrap may be inconsistent. This problem is usually solved by recentering either the residuals, the sample estimating equations, or the statistic of interest.; In this dissertation, we developed a new biased bootstrap methodology for moment condition models. This biased bootstrap is a form of weighted bootstrap with the weights chosen to satisfy the constraints imposed by the model. First, we construct a pseudo-parametric family of weighted empirical distributions, obtained by minimizing the Cressie-Read distance to the empirical distribution under the constraints imposed by the model. The resulting family has the least favorable property, meaning that the inverse of the Fisher information matrix evaluated at the MLE equals the sandwich estimator. By resampling within this family, we "mimic" the parametric bootstrap for semiparametric models. An extension of this methodology for time series applies the biased bootstrap to the sample of blocks of consecutive observations.; Our overall goal is to extend and develop the range of applications and theoretical properties of the biased bootstrap, focusing mainly in three directions. First, we prove that the biased bootstrap is consistent in moment condition models, with no need for "recentering". Moreover, by applying bootstrap recycling within the pseudo-parametric family, we obtain computationally feasible and more accurate iterated biased bootstrap procedures. The main idea here is to reuse the first level bootstrap resamples in order to estimate higher level parameters corresponding to the iterated bootstrap. Third, new biased bootstrap procedures are proposed for problems where the usual uniform bootstrap fails, such as on the boundary of the parameter space and for certain asymptotically nonnormal statistics. |
